A new adaptive modification strategy for numerical solutions to elliptic boundary value problems Original Research Article

An h–p adaptive spectral element method for elliptic problems featuring simultaneous h and p refinements is presented. Results obtained by applying this strategy to the Helmholtz equation for different orders of regularity of the solution are compared to the results obtained using the 3-step h–p adaptive strategy of Oden et al. (1992). Theoretical reasons for deficiencies in Odenʹs 3-step strategy are presented. The results obtained in terms of computational CPU-time and global number of degrees of freedom show the advantages of using the new approach.